This article is the first part of a review of the theory of wave phenomena in plasmas. The basic kinetic theory is developed taking into account coulomb collisions. From this magnetohydrodynamic equations are derived. It is demonstrated that it is legitimate to deal with a closed subset of these equations either in the limit of collision-dominated phenomena, or in the limit where the effective phase velocities of the phenomena of interest are much greater than thermal speeds. In case of collision-dominated plasmas the theory of transport coefficients is discussed.These equations are then applied to an extensive treatment of small amplitude wave phenomena in plasmas. A discussion of the dissipative effects on hydromagnetic waves is given. Hydromagnetic waves are also considered from the Chew, Goldberger and Low theory. Longitudinal and transverse oscillations in current-carrying plasmas are also discussed.Oscillations of a cylindrical plasma are considered and the phenomenon of ion cyclotron resonance is discussed. The possibility of radiation by plasma oscillations by a uniform sphere is exhibited. Some general results on the stability of longitudinal electron oscillations in non-uniform plasmas are given.A brief treatment of large amplitude electron oscillations is given and the breaking of these oscillations as a dissipative mechanism for the organized plasma motion is discussed.Part II of this paper, to appear in a future issue of this journal, will be devoted to the discussion of plasma oscillations directly from the kinetic theory.
This work is the second part (and chapter VI) of a three-part series reviewing the subject of plasma oscillations. Part I (Nuclear Fusion 1 (1960) 3) was devoted to the macroscopic theory of plasmas in general, and plasma waves in particular, in both collision-free and collision-dominated plasmas, with and without magnetic fields, in some cases with boundaries and spatial gradients. The present article is concerned mostly with the kinetic theory of collision-free plasmas in the absence of magnetic fields, boundaries and spatial gradients and with neglect of the coupling with the radiation field. It is this area that has been most extensively expounded and that can be adapted to a heuristic theory of the non-equilibrium statistical mechanics of plasmas.The plan of the work is as follows: First the small longitudinal oscillations of an infinite homogeneous collisionless plasma are considered. Clearly the model requires that the frequency of collisions, Coulomb or other, be much smaller than the characteristic frequencies and growth rates of the system. The general theory is applied to an investigation of the stability of such systems and the polarization of its environment by a test charge. The latter provides the basic data for a heuristic theory of the non-equilibrium statistical mechanics of plasmas, which yields, for instance, a derivation of the Fokker-Planck equation with polarization corrections and a treatment of fluctuation phenomena in plasmas. This last is applied to the theory of the experimentally interesting phenomenon of the scattering of light by plasmas.The phenomenon of Landau damping has been treated both by the Laplace-transform technique and the normal-mode technique, and the equivalence of both methods has been shown. A special class of finite-amplitude electrostatic waves has been treated, and its relation to the normal modes of the linearized equations has been given. Also plasma oscillations of a large number of electron beams are considered, and the limit of an infinite number of beams is shown to yield the results of a plasma with a continuous velocity distribution.Part III of this series will deal with the effects of magnetic fields, relativity and coupling with the radiation field on the kinetic and non-equilibrium statistical-mechanical theories.
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It has been recently pointed out by Hosking 1 that the inclusion of Hall current in Ohm's law produces a new aperiodic instability in a wave number band which was previously stable in the classical problem of Rayleigh-Taylor instability for a plasma. 2 ' 3 However, it will be shown here that this result is incorrect and is a consequence of the fact that Hosking has not solved the problem with due regard to the boundary conditions. It is the aim of this note to show that the inclusion of Hall-current and electron-inertia terms in the generalized Ohm's law, in fact, do not have any effect on the development of Rayleigh-Taylor instability in hydromagnetics.Consider then a situation where an infinitely conducting plasma occupies the half-space 0
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